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We are given the following angles in the diagram:

- \( m \angle IJL = 96^\circ \)
- \( m \angle LJK = 70^\circ \)

We are tasked with solving for \( m \angle IJK \).

### Explanation:
From the diagram, we can observe that the points \( I, J, L, K \) form a straight path, which implies that:

\[
m \angle IJL + m \angle LJK = m \angle IJK
\]

This is because the three angles are adjacent and must sum to form a straight line, which is \( 180^\circ \).

So, the equation becomes:

\[
m \angle IJK = m \angle IJL + m \angle LJK = 96^\circ + 70^\circ = 166^\circ
\]

Thus, \( m \angle IJK = 166^\circ \).

Would you like any further details on this solution, or do you have any additional questions?

Here are five follow-up questions to explore this concept further:
1. How do we know that angles on a straight line add up to \(180^\circ\)?
2. What would happen if one of the angles was unknown? How would we solve for it?
3. Can you describe how adjacent angles work in different types of geometric figures?
4. What is the difference between supplementary and complementary angles?
5. How do we use the concept of straight angles in solving more complex geometric problems?

**Tip**: When dealing with geometry problems, always look for known relationships like supplementary angles or triangle sum properties to break down the problem more easily!

Solve for m∠IJK if m∠IJL = 96° and m∠LJK = 70°.

Learn how to solve for the angle m∠IJK in a geometry problem where points form a straight line. Given m∠IJL = 96° and m∠LJK = 70°, find the value of m∠IJK using angle addition and straight angle theorems. Suitable for Grades 6-8.

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